State Feedback H₂/H_∞Control Of Switched Systems

Switched systems are composed of several subsystems under the corresponding switching laws which contains the continuous dynamic process and discrete dynamic process. The switched systems overcome the disadvantages of using a single controller so that they are more applicable to complex engineering application by using feasible switching strategy.H∞norm and H∞norm are two important performance indexes in control theory.H2/H∞Hr control theory can be obtained by combining H∞control and Hx control theory. In engineering practice, H2/H∞Hy hybrid control not only reduces the conservatism of the H∞control, but also makes the system maintain better control performance. The stability of a system is the precondition of maintaining normal operation of the system. This paper will discuss H2/H∞Hx hybrid control problems of a class of switched systems with different types of disturbances. The main research contents are as follows:The problem of stability of the switched systems under the appropriate switching law is discussed, and also the problem of solvability of the system state feedback control of H2/H∞. Two sufficient conditions for the switched systems are derived by using single Lyapunov functions method and multiple Lyapunov functions method respectively. Controllers of satisfying different requirements of the state feedback H2/H∞problems are designed.The solvability problem of state feedback control of H2/H∞of switched time-delay systems, a sufficient condition is obtained and the method of designing switching law is given. Based on multiple Lyapunov functions theory, state feedback controllers of H2/H∞control are designed and the solvability of a class of switched time-delay systems state feedback control of H2/H∞is obtained.The problem of robust stability of switched time-delay systems with uncertain parameters is discussed. Using multiple Lyapunov functions method, state feedback controllers of H2/H∞are designed and the sufficient condition of the solvability of the switched time-delay systems state feedback control of H2/H∞is given. The last, the research achievements of this paper are summarized, and the future research direction is pointed out.